SSC CGL 2025 Tier-I · 17 September 2025, Shift 1 · Quantitative Aptitude · Question 8 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

Rs. 900 is lent at a certain rate of simple interest. After 9 months, another Rs. 600 is lent at a rate that is 1.5 times the original rate. If the total simple interest after 1 year is Rs. 72, find the original rate.

(a)6.4%
(b)4.5 %
(c)8.2%
(d)5.6%

Answer

Why

Correct — A. Let the original rate be r%. Counting 1 year from the first loan, Rs. 900 is out for 12 months and Rs. 600 for only the last 3 months.

Rs. 900 for 1 year: 900 × r × 1 ÷ 100 = 9r
Rs. 600 at 1.5r for 3⁄12 year: 600 × 1.5r × (3⁄12) ÷ 100 = 2.25r
Total: 9r + 2.25r = 11.25r = 72
Divide: r = 72 ÷ 11.25 = 6.4

Original rate = 6.4% → option (a)

Why the others are wrong

(b)
4.5 % — 4.5%: Rs. 900 earns Rs. 40.50, and Rs. 600 at 6.75% for 3 months earns about Rs. 10.13. The total, about Rs. 50.63, falls short of Rs. 72.
(c)
8.2% — 8.2% overshoots: 11.25 × 8.2 = Rs. 92.25 of interest, Rs. 20.25 more than the Rs. 72 given.
(d)
5.6% — 5.6% gives 11.25 × 5.6 = Rs. 63 of interest, Rs. 9 short of Rs. 72.

Concept

Simple interest is P × R × T ⁄ 100, and T counts only the time each sum is actually out. When a second sum is lent partway through, give each sum its own time.

The Rs. 600 starts after 9 months, so by the 1-year mark it has earned for 3 months = 1⁄4 year, at 1.5 times the first rate.

The total interest is the sum of the two separate interests.

If the Rs. 600 earned for a full year as well, 9r + 9r = 72 would give r = 4%, which is not among the options. The key times both loans from the start, leaving the Rs. 600 out for 3 months.

Key facts

Simple interest = P × R × T ⁄ 100, with T in years.
Months convert to years by dividing by 12: 3 months = 1⁄4 year.
At r = 6.4%, the second rate is 1.5 × 6.4% = 9.6%.

Study next

Simple interest for periods given in months or daysSums lent at different times and different ratesPartnership with capital added or withdrawn midway

Common traps

Giving the Rs. 600 the full year. It is lent after 9 months, so it earns for 3 months.
Charging the Rs. 600 at the original rate instead of 1.5 times it.

The months-to-years step on its own is 12 Sep 2024, 16:00, Quant Q.5: ₹6,700 for 13 months at 12% earns 6700 × 12 × (13⁄12) ÷ 100 = ₹871.

Related PYQs

No directly related past PYQ was found.

Topic: Interest — all 82 SSC CGL questions on it, every solved shift.